Terminal procedures, covering the takeoff and landing phases, form the subject of research aimed at decreasing environmental nuisance, in particular noise or emissions of pollutant or greenhouse effect gases. The approach procedures customarily implemented generally comprise an alternating series of descent segments and of plateaus of constant altitude. Such an approach procedure is shown diagrammatically in FIG. 1 by the trajectory referenced 10. The plateaus 11 carried out at constant altitude allow the air traffic control to monitor and separate the aircraft from the relief or from other aircraft. They also make it possible to perform diverse maneuvers, such as reduce the aircraft speed or modify its aerodynamic configuration (deploy the slats, the flaps, the airbrakes) while safeguarding passenger comfort.
Alternative procedures to this plateau-based approach are envisaged. CDA procedures, the acronym standing for Continuous Descent Approach, are known for example, their aim being to descend towards the landing runway while maintaining reduced thrust so as to minimize nuisance (noise and pollution). Accordingly, it is sought to maintain the aircraft under reduced thrust, or IDLE thrust regime according to the terminology of the art, for as long as possible, between a descent start point and an exit point beyond which the reduced thrust can no longer be upheld in order to allow the aircraft to land. A CDA procedure without vertical constraint, or CDA-SCV, is represented by the trajectory 12 in FIG. 1. The aircraft is maintained under reduced thrust on this trajectory for as long as possible, and without any constant altitude plateau. A CDA procedure with vertical constraint, or CDA-PVC, is represented by the trajectory 13. In this case, the descent is also carried out under idle regime but also takes account of possible vertical constraints, in terms of altitude and/or speed at one or more intermediate points between the descent start point and the exit point.
Procedures referred to as “green” in the terminology of the art, for which the reduced-thrust descent procedures make it possible to reduce the emissions of pollutants and of greenhouse effect gases, are also known. By maintaining the idle regime for as long as possible, fuel consumption is reduced accordingly, as are airline operating costs. These reduced-thrust descent procedures and their implementations are explained in detail hereinafter.
FMS Systems of the Prior Art
Diverse systems exist for aiding a crew in the piloting of an aircraft notably during an approach phase. Known in particular among these systems are flight management systems (FMS), shown diagrammatically in FIG. 2 and comprising the following functions:                Location LOCNAV, labelled 1: making it possible to locate the aircraft by means of diverse geolocation tools or instruments (GPS, GALILEO, VHF radio beacons, inertial platforms),        Flight plan FPLN, labelled 2: making it possible to input the geographical elements constituting the skeleton of the route to be followed (departure and arrival procedures, waypoints, etc.),        Navigation database NAVDB 3: making it possible to construct geographical routes and procedures on the basis of data included in the bases (points, beacons, interception or altitude legs, etc.),        Performance database PRF DB 4: containing the craft's aerodynamic and engine parameters,        Lateral trajectory TRAJ 5: making it possible to construct a continuous trajectory on the basis of the points of the flight plan, complying with the aeroplane performance and the confinement constraints,        Predictions PRED 6: making it possible to construct an optimized vertical profile compatible with the lateral trajectory,        Guidance GUIDANCE 7: making it possible to guide the aircraft on its 3D trajectory in the lateral and vertical planes, while optimizing the speed,        Digital datalink DATALINK 8: making it possible to communicate with control centres, airlines and other aircraft.Flight Plan & Vertical Constraints        
A flight plan defined by the pilot comprises a list of waypoints characterized notably by lateral and vertical geographical coordinates, speed constraints and/or transit time constraints. FIG. 3 illustrates a conventional flight plan of an aircraft 20 proceeding towards a landing runway at a landing point 21, and comprising a sequence of waypoints WPTi. On the basis of these waypoints, the FMS determines a target trajectory for the aircraft, consisting of a series of segments 22 connecting two successive waypoints. The trajectory is generally split between a lateral trajectory, determined by the TRAJ function 5, and a vertical trajectory, determined by means of the PRED function 6. In FIG. 3 is represented the lateral trajectory, referenced PP.
The constraints in terms of altitude, speed or waypoints transit time can be expressed in diverse ways. The following are known in particular:                altitude constraints, for example of the “AT” (transit the point at the given altitude), “AT OR ABOVE” (transit at or above the given altitude), “AT OR BELOW” (transit at or below the altitude) or “WINDOW” (transit between two altitudes) type,        speed constraints, for example of “AT” (transit the point at the given speed), “AT OR FASTER” (transit at or above the given speed), “AT OR LESS” (transit at or below the speed) or “WINDOW” (transit between two speeds) type, and        time constraints, for example of “AT” (transit the point at the given time), “AT OR AFTER” (transit at or after the given time), “AT OR BEFORE” (transit at or before the given time) or “WINDOW” (transit between two times) type.        
Note that the speed constraints are generally defined in terms of conventional speed referred to as CAS, the acronym standing for Calibrated Air Speed. This does not constitute a limitation of the present invention which applies more generally to any type of speed constraint, for example expressed in terms of Mach number, air speed referred to as TAS the acronym standing for True Airspeed, or else in terms of ground speed referred to as GS the acronym standing for Ground Speed; all these speeds being well known to the person skilled in the art.
Other constraints exist and are not related to a given waypoint. It is possible to cite the “SPEED LIMIT” or “descent speed limit” which represents a speed not to be exceeded below a given altitude for reasons of noise and traffic sequencing in proximity to airports. For most airports around the world, this speed is 250 kts (kts=knots, i.e. about 130 m/s or 460 km/h) below 10,000 ft (ft=feet, i.e. about 3050 m). Other types of speed or altitude constraints can also exist such as constraints in terms of speed at a certain distance from the runway.
Descent and Approach Profiles
FIGS. 4a, 4b, 4c, 4d, 4e and 4f illustrate several typical descent profiles in terms of altitude and speed. For all these figures, the altitude profile is represented in the upper part of the figure, and the speed profile is represented in the lower part. The speed profile is represented in terms of conventional speed CAS. The abscissa represents the distance DtD (the acronym standing for “Distance To Destination”) separating the aircraft from the landing point 21 represented on the extreme right of the figure.
Before describing these various conventional descent profiles in detail, let us recall through a few equations the principles of the vertical evolution of an aircraft in flight. The vertical evolution of a fixed-wing aircraft can be defined by the following equation of dynamics:
                              ∑                                          ⁢                                    F              →                        ext                          =                  m          ·                                    ⅆ                              V                →                                                    ⅆ              t                                                          (        1        )            in which Fext represents the exterior forces applied to the aircraft, m the mass of the aircraft, and V its speed.
Under projection onto two horizontal and vertical axes, equation (1) is expressed by the following two equations:                in the horizontal plane:        
                              m          ·                                    ⅆ              V                                      ⅆ              t                                      =                  Tx          -          Fx          -                                    mg              ·              sin                        ⁢                                                  ⁢            γ                                              (        2        )                            and in the vertical plane:Fz=mg·cos γ  (3)in which Tx is the thrust, Fx is the drag, Fz is the lift, and γ is the aerodynamic slope.        
The lift can be expressed by the relation:Fz=½ρ·S·Vair2·Cz  (4)in which ρ is the density of the air, S the aerodynamic surface area, Vair the air speed and Cz the lift coefficient.
Likewise, the drag can be expressed by the relation:Fx=½ρ·S·Vair2·Cx  (5)in which Cx is the drag coefficient.
The drag and the lift of the aircraft are related by one and the same aerodynamics of the aircraft. The coefficients of lift Cz and of lift Cx are therefore related by an equation of the type:Cx=f(Cz)  (6)
The drag coefficient Cx can generally be determined in an empirical manner, by means of numerical computations or prior wind tunnel trials. This coefficient can generally be expressed by means of a relation of the type:Cx=f(Cx—smooth;Cx—conf(i) with i=1 . . . Nconf;Cx—m)  (7)in which Cx—smooth represents the drag of the aircraft in the case where the aircraft is in so-called smooth configuration, that is to say when the slats, flaps, airbrakes and landing gear are retracted; Cx—conf(i) with i=1 . . . Nconf represents the additional drag in the various possible aerodynamic situations during approach, that is to say with the slats, and/or the flaps, and/or the airbrakes and/or the landing gear deployed; and Cx—m represents the drag induced by the aircraft mass; the function “f” generally being a simple weighted sum of the various coefficients.
It is known finally that the aircraft position, lateral (x) and vertical (z), can be computed by integration as a function of the speed V and of the aerodynamic slope γ by means of the following two relations:dx/dt=V·cos γ, and dz/dt=V·sin γ  (8)
To summarize, the three variables speed V, aerodynamic slope γ and thrust Tx, are connected by two equations (the equations referenced (2) and (3)). A relationship therefore exists between these three quantities. In practice, this signifies that the piloting of the aircraft in the vertical plane can be carried out by fixing two variables, the third being deduced from the equations described hereinabove. Several modes of control in the vertical plane are thus implemented:                fixed thrust and imposed speed mode; the resultant being the slope,        fixed slope and imposed speed mode; the resultant being the thrust,        fixed slope and imposed thrust mode; the resultant being the speed,        fixed thrust and imposed acceleration/deceleration mode; the resultant being the slope.        
Other modes of control, not implemented in avionics suites today, could be envisaged without departing from the scope of the present invention.
FIG. 4a represents a first conventional descent profile in terms of altitude and speed. The profile represents the target vertical trajectory of the aircraft between the descent start point and the landing runway 21. The descent start point, referenced T/D the acronym standing for Top of Descent, is characterized by a distance T/D Dist separating it from the landing point 21, an altitude CRZ ALT, and a speed CRZ MACH. In the cruising phase preceding the point T/D, the aircraft is generally in a smooth configuration.
Onwards of this point, the descent and the deceleration are carried out in several steps until the landing point 21 is reached at an altitude RWY ALT and for a landing speed VAPP.
This first descent profile comprises three successive segments:                A first segment 25 carried out at imposed speed and fixed thrust. On this segment, the descent is in general performed in two portions: a first portion on which the descent is performed at an imposed speed MACH equal to the speed DES MACH, and a second portion on which the descent is performed at an imposed speed CAS equal to DES CAS. The speed transition between the two portions is carried out at an altitude XOVER ALT for which the air speed (TAS) corresponding to DES MACH is equal to the air speed corresponding to DES CAS. Thus, the change of speed mode from MACH to CAS is performed at one and the same air speed and there is therefore no change of engine regime.        
This segment 25 is in general carried out with the idle regime (IDLE). Typically, the aeroplane lets itself drop at fixed thrust while modifying its attitude (i.e. raising or lowering its nose) so as to submit itself in regard to the speed (DES MACH on the first portion, then DES CAS on the second portion). As explained above, the resultant of this fixed-thrust and imposed-speed piloting mode is the aerodynamic slope. A slightly greater slope is noted on the MACH segment. This is explained by the fact that the slope increases with the speed CAS, and that at constant MACH, the CAS increases as the altitude decreases.                A second segment 26, the aim of which is to reach a point DECEL of predetermined altitude and speed, respectively FCA ALT and SPDLIM CAS, with as constraint a speed less than or equal to SPDLIM CAS for an altitude less than an intermediate altitude SPDLIM ALT. On the basis of this dual-constraint of the arrival point DECEL and of the intermediate point, the FMS systems determine by iterative computations the point 27 onwards of which it is necessary to begin the deceleration, or stated otherwise the point of transition between the segments 25 and 26. This point 27 of change of speed is labelled by distance at SPDCHG Dist and/or by altitude at SPDCHG ALT.        A third segment 28 onwards of which the crew must begin to engage the aerodynamic approach configurations, by deploying the slats, and/or the flaps, and/or the landing gear, and/or the airbrakes. The aim of the third segment is to reach the landing point 21 from the DECEL point. A first portion 28a of the latter segment is carried out at constant altitude, making it possible to stabilize the aircraft during the phase of engaging the aerodynamic approach configurations. The approach terminates with a last portion 28b in the course of which the aircraft reaches the runway in general with imposed slope.        
This cutting into three segments makes it possible to illustrate the principal steps of this descent profile, typical in aeronautics. In the known state of the art, one also speaks of “descent phase” or DES PHASE for the part preceding the DECEL point (i.e. the segments 25 and 26), and of “approach phase” or APP PHASE for the part following the DECEL point (i.e. the segment 28). The approach phase corresponds to a phase where the dynamic configuration is not smooth. The two portions of the segment 28, referenced 28a and 28b respectively, are dubbed “intermediate approach” or INT APP, and “final approach segment” or FINAL APP respectively, and correspond respectively to the portion carried out at constant altitude and to the portion carried out at constant slope.
On this first descent profile represented in FIG. 4a, the descent phase and the intermediate approach phase can be carried out in the idle regime. On the other hand, the final approach is in the computed regime, the slope and the speed being fixed. This vertical profile is very widespread and regularly implemented on commercial aircraft in the phase of descent and approach to the landing runway. This profile corresponds to the trajectory 10 of FIG. 1 described in the preamble.
FIG. 4b represents a second conventional descent profile in terms of altitude and speed. This profile exhibits numerous points in common with the first profile described in FIG. 4a which will not be repeated here in detail. The aim of this second profile is to remove the plateaus of constant altitude carried out at low altitude. Accordingly the DECEL point is shifted so as to allow an approach deceleration, between the DECEL point and the landing point 21, carried out in the idle regime (the resultant is therefore the slope). Stated otherwise, the segment 29 does not comprise any plateau. The intermediate approach segment 29a, in the course of which the aerodynamic configuration is modified, is carried out at decreasing altitude, contrary to the intermediate approach segment 28a in FIG. 4a. This second descent profile therefore corresponds to the trajectory 12 of FIG. 1 described in the preamble. This is the typical descent profile of a CDA (“Continuous Descent Approach”) descent without vertical constraint. Such a descent makes it possible to limit the nuisance (sound, pollutants, etc.) in proximity to the landing runway by removing the plateaus carried out at low altitude.
FIG. 4c represents a third descent profile in terms of altitude and speed. As previously, the points in common with the profiles described in FIGS. 4a and 4b are not repeated in detail. Note that the profiles of FIGS. 4a and 4b are represented in FIG. 4c respectively by the dashed and dotted trajectories 30 and 31. This third profile comprises a vertical constraint at a point WPT6 situated between the descent start point T/D and the DECEL point. In this example, the vertical constraint is of “AT OR ABOVE” type in terms of altitude, the aircraft having to transit the point WPT6 at an altitude greater than or equal to WPT6 ALT, and of “AT OR LESS” type in terms of speed, the aircraft having to transit the point WPT6 at a speed less than or equal to WPT6 SPD. Commencing from the profiles such as described by FIGS. 4a and 4b, the descent profile is modified, for example by the addition of the following two segments:                A change-of-speed segment 32, carried out at fixed thrust and imposed acceleration/deceleration, connecting a point SPDCHG to the waypoint WPT6; the point SPDCHG being determined so as to comply with the vertical constraint at the point WPT6.        A segment 33 carried out at fixed slope and imposed speed beyond the point WPT6. The slope is bigger than that resulting from the idle regime IDLE so as to make it possible to regain the descent profile 30 at the second point SPDCHG making it possible to comply with the dual-constraint, described in FIG. 4a, of the DECEL point. This segment 33 with large slope and imposed speed makes it necessary to maintain a minimum thrust (with the idle regime IDLE) and a modification of the aerodynamic configuration (for example deployment of the airbrakes) so as to be able to maintain the speed, without which the aircraft would accelerate.        
On this descent profile, the point WPT6 is therefore the point marking the end of the IDLE section, one generally speaks of “last IDLE point”. The aircraft is in the smooth configuration and at fixed IDLE thrust before this point. Beyond this point, the descent becomes geometric: the aircraft is at a thrust potentially greater than the IDLE and the aerodynamic configuration may possibly be modified. The sound nuisance and the emissions of pollutants beyond this point are therefore more significant.
FIG. 4d represents a fourth descent profile in terms of altitude and speed. As previously, the profiles of FIGS. 4a and 4b are represented respectively by the dotted and dashed trajectories 30 and 31. This fourth profile comprises a vertical constraint at a point WPT5 of “AT OR BELOW” type in terms of altitude. In certain known FMS systems, this vertical constraint is taken into account by adding to the descent profile 30 such as described by FIG. 4a a segment 35 carried out onwards of the point WPT5. The segment 35 is carried out at fixed slope, a lower slope than the IDLE slope so as to regain the descent profile 30, and at imposed speed, the speed DES CAS. The resultant is a greater thrust than the IDLE reduced thrust, making it possible to maintain a constant speed up to the point SPD CHG, without which there would be deceleration.
Stated otherwise, the introduction of a vertical constraint of “AT OR BELOW” type in terms of altitude at the point WPT5 is taken into account by the FMS, by the addition of a segment making it necessary to leave the idle regime IDLE beyond this point, with here again as corollary an increase in noise and emissions of pollutants. The point WPT5 is the “last IDLE point”. Faced with this type of vertical constraint, other FMS systems adapt the descent profile in a slightly different manner as described in the following figure.
FIG. 4e represents a fifth descent profile in terms of altitude and speed. Just as for FIG. 4d, this fifth profile comprises a vertical constraint at the point WPT5 of “AT OR BELOW” type in terms of altitude. In this case, the vertical constraint is taken into account by adding to the descent profile 30 such as described by FIG. 4a two successive segments 36 and 37, carried out onwards of the point WPT5. The segment 36 is carried out at constant altitude (zero fixed slope) and at imposed speed. It therefore requires a greater thrust than the IDLE reduced thrust. The following segment 37 is carried out at fixed thrust equal to the IDLE thrust and at imposed speed. This segment is carried out provided that the aircraft has reached the profile 30, that is to say provided that there has been a return to a reduced-thrust descent.
Stated otherwise, the introduction of a vertical constraint of “AT OR BELOW” type in terms of altitude at the point WPT5 is taken into account by the FMS, by the addition of a first segment with increased thrust making it possible to regain as quickly as possible a descent profile with IDLE thrust. As in the profile described by FIG. 4d, the point WPT5 is the “last IDLE point”.
FIG. 4f represents a sixth descent profile in terms of altitude and speed. This profile associates the two vertical constraints introduced previously, that is to say a constraint at the point WPT5 of “AT OR BELOW” type in terms of altitude, and a constraint at the point WPT6 of “AT OR ABOVE” type in terms of altitude and “AT OR LESS” type in terms of speed. In known FMS systems, the descent profile making it possible to comply with these vertical constraints combines the segments of the descent profiles described by FIGS. 4c and 4d (or 4c and 4e). Thus, commencing from the profile 30 such as described in FIG. 4a, the modifications consist in adding:                A plateau segment 40 after the point WPT5, with zero slope and imposed speed, until the point where the descent can be continued with IDLE thrust.        A segment 41 at fixed thrust equal to the IDLE thrust, and at imposed speed. These two segments 40 and 41 make it possible to comply with the vertical constraint at the point WPT5 according to a similar strategy to that described in FIG. 4e.         A segment 42 of change of speed before the point WPT6, carried out onwards of the point SPD CHG, and for a fixed thrust and an imposed acceleration/deceleration.        A segment 43 at fixed slope and imposed speed after the point WPT6, and with a greater slope than the slope obtained in IDLE, rendered necessary for compliance with the altitude constraint at the point WPT6. Accordingly, an IDLE thrust is invoked, combined with a deployment of the airbrakes. These last two segments 42 and 43 make it possible to comply with the vertical constraint at the point WPT6 according to a similar strategy to that described in FIG. 4c.         
Thus, the two vertical constraints at the points WPT5 and WPT6 have been able to be taken into account successively. To comply with each constraint, specific maneuvers are necessary. In this example, compliance with the vertical constraint at WPT5 imposes a segment 40 on which the IDLE thrust is not upheld, compliance with the constraint at WPT6 imposes a segment 43 on which the airbrakes are used. The point WPT5 is the “last IDLE point”.
The typical descent profiles described by FIGS. 4a to 4f make it possible to illustrate the operating principle of the descent procedures implemented in current FMS systems. This also makes it possible to highlight the limits of known FMS systems, in particular in the case where vertical constraints must be taken into account in the descent and approach phase. Each vertical constraint being taken into account in an individual manner, the maneuvers making it possible to comply with each constraint are engaged successively without taking into account the whole set of constraints. In general, the maneuvers engaged lead to the reduced thrust mode being quit.
It is therefore desirable to have a means for computing a vertical descent trajectory capable of optimizing the CDA procedure, that is to say of maximizing the length of the segment carried out at reduced thrust and in the smooth aerodynamic configuration, between the descent start point and the point beyond which the reduced thrust cannot be upheld. It is also desirable to maximize the number and the length of the segments carried out at reduced thrust that can be integrated into the descent and approach procedure up to the landing point. Finally, it is also desirable to maximize the length of the segment carried out at reduced thrust and in the aerodynamic configuration deployed, between the start point of the approach and the runway.